22 citations · 51 across the 10 of their papers we have counts for
13 papers
A proof of the Multiplicative 1-2-3 Conjecture
Julien Bensmail, Hervé Hocquard, Dimitri Lajou +1
We prove that the product version of the 1-2-3 Conjecture, raised by Skowronek-Kazi{ó}w in 2012, is true. Namely, for every connected graph with order at least 3, we prove that we…
Complexity and algorithms for injective edge-coloring in graphs
Florent Foucaud, Hervé Hocquard, Dimitri Lajou
An injective -edge-coloring of a graph is an assignment of colors, i.e. integers in , to the edges of such that any two edges each incident with one d…
On a List Variant of the Multiplicative 1-2-3 Conjecture
Julien Bensmail, Hervé Hocquard, Dimitri Lajou +1
The 1-2-3 Conjecture asks whether almost all graphs can be (edge-)labelled with so that no two adjacent vertices are incident to the same sum of labels. In the last decades…
Between proper and strong edge-colorings of subcubic graphs
Hervé Hocquard, Dimitri Lajou, Borut Lu{ž}ar
In a proper edge-coloring the edges of every color form a matching. A matching is induced if the end-vertices of its edges induce a matching. A strong edge-coloring is an edge-colo…
Exact square coloring of subcubic planar graphs
Florent Foucaud, Hervé Hocquard, Suchismita Mishra +4
We study the exact square chromatic number of subcubic planar graphs. An exact square coloring of a graph G is a vertex-coloring in which any two vertices at distance exactly 2 rec…
Further Evidence Towards the Multiplicative 1-2-3 Conjecture
Julien Bensmail, Hervé Hocquard, Dimitri Lajou +1
The product version of the 1-2-3 Conjecture, introduced by Skowronek-Kazi{ó}w in 2012, states that, a few obvious exceptions apart, all graphs can be 3-edge-labelled so that no two…
Graph modification for edge-coloured and signed graph homomorphism problems: parameterized and classical complexity
Florent Foucaud, Hervé Hocquard, Dimitri Lajou +2
We study the complexity of graph modification problems with respect to homomorphism-based colouring properties of edge-coloured graphs. A homomorphism from edge-coloured graph …
A Connected Version of the Graph Coloring Game
Eric Sopena, Clément Charpentier, Hervé Hocquard +1
The graph coloring game is a two-player game in which, given a graph G and a set of k colors, the two players, Alice and Bob, take turns coloring properly an uncolored vertex of G,…
Coloring squares of graphs with mad constraints
Hervé Hocquard, Seog-Jin Kim, Théo Pierron
A proper vertex -coloring of a graph is an assignment of colors to the vertices of the graph such that no two adjacent vertices are associate…
On the total neighbour sum distinguishing index of graphs with bounded maximum average degree
Hervé Hocquard, Jakub Przybyło
A proper total -colouring of a graph is an assignment of colours to the edges and the vertices of such that no two adjacent edge…
On the neighbour sum distinguishing index of graphs with bounded maximum average degree
Hervé Hocquard, Jakub Przybyło
A proper edge -colouring of a graph is an assignment of colours to the edges of the graph such that no two adjacent edges are associated with…
Incidence coloring of graphs with high maximum average degree
Marthe Bonamy, Hervé Hocquard, Samia Kerdjoudj +1
An incidence of an undirected graph G is a pair where is a vertex of and an edge of incident with . Two incidences and are adjacent if on…
Strong edge-colouring of sparse planar graphs
Julien Bensmail, Ararat Harutyunyan, Hervé Hocquard +1
A strong edge-colouring of a graph is a proper edge-colouring where each colour class induces a matching. It is known that every planar graph with maximum degree has a strong e…